What technology do people use to create bots for games like LOL or Runescape?
Bot development is more about 'hacking' than AI in a way that in the very first place you need to read and (over) write game data which you are not supposed to (and thereby potentially violating the Terms and Conditions - so be aware of that). The AI part is fairly simple for most hack/bot applications that I can think of. 

Read data

To read game data you can for example:


use an assembly code debugger like Ollydbg to locate relevant data in the memory, e.g. amount of gold
Observe graphical objects being rendered, e.g. a unit being drawn
Intercept network packages containing all kinds of game information, e.g. a unit appearing on your screen


Write data

In a similar way there are multiple ways to write data:


overwrite game data in memory
Use the Windows API SendInput() function to emulate keyboard inputs
Use the Windows API SendMessage() function to send messages to the game
Manipulate network traffic


These lists are not comprehensive but to give you an idea of how it is being done. 

AI-wise an A* algorithm for example can be deployed to do path finding. 

If you are interested in the topic I suggest to read 'Game Hacking' by Nick Cano. The book provides a good introduction.